Solve for $x$ and $y$ using elimination. ${-4x+2y = -8}$ ${-3x-2y = -41}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-7x = -49$ $\dfrac{-7x}{{-7}} = \dfrac{-49}{{-7}}$ ${x = 7}$ Now that you know ${x = 7}$ , plug it back into $\thinspace {-4x+2y = -8}\thinspace$ to find $y$ ${-4}{(7)}{ + 2y = -8}$ $-28+2y = -8$ $-28{+28} + 2y = -8{+28}$ $2y = 20$ $\dfrac{2y}{{2}} = \dfrac{20}{{2}}$ ${y = 10}$ You can also plug ${x = 7}$ into $\thinspace {-3x-2y = -41}\thinspace$ and get the same answer for $y$ : ${-3}{(7)}{ - 2y = -41}$ ${y = 10}$